A new high-order particle method for solving high Reynolds number incompressible flows

Rex Kuan Shuo Liu, Khai Ching Ng, Tony Wen Hann Sheu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this study, a new high-order particle method is proposed to solve the incompressible Navier–Stokes equations. The proposed method combines the advantages of particle and mesh methods to approximate the total and the spatial derivative terms under the Lagrangian and the Eulerian frameworks. Our aim is to avoid convective instability and increase solution accuracy at the same time. Data transfer from Lagrangian particles to Eulerian grids is realized by moving least squares interpolation. In contrast to the previously proposed method, there is no need to interpolate diffusion terms from Eulerian grids to Lagrangian particles. Therefore, the accuracy of the present solution will not be deteriorated by interpolation error. Additionally, no extra work is required to manage particles for searching procedure. Because no convection term needs to be discretized by upwinding schemes, false diffusion and dispersion errors will not be introduced, thereby increasing the solution accuracy. To verify the proposed particle method, several benchmark problems are solved to show that the present simulation is more stable, accurate, and efficient. The proposed particle method renders fourth- and second-order accurate solutions in space for velocity and pressure, respectively.

Original languageEnglish
Pages (from-to)343-370
Number of pages28
JournalComputational Particle Mechanics
Volume6
Issue number3
DOIs
Publication statusPublished - 15 Jul 2019

Fingerprint

Particle Method
High-order Methods
Incompressible flow
Incompressible Flow
Reynolds number
Interpolation
Data transfer
Term
Interpolate
Convective Instability
Grid
Derivatives
Upwinding
Incompressible Navier-Stokes
Interpolation Error
Moving Least Squares
Data Transfer
Convection
Fourth Order
Navier-Stokes Equations

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Civil and Structural Engineering
  • Numerical Analysis
  • Modelling and Simulation
  • Fluid Flow and Transfer Processes
  • Computational Mathematics

Cite this

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abstract = "In this study, a new high-order particle method is proposed to solve the incompressible Navier–Stokes equations. The proposed method combines the advantages of particle and mesh methods to approximate the total and the spatial derivative terms under the Lagrangian and the Eulerian frameworks. Our aim is to avoid convective instability and increase solution accuracy at the same time. Data transfer from Lagrangian particles to Eulerian grids is realized by moving least squares interpolation. In contrast to the previously proposed method, there is no need to interpolate diffusion terms from Eulerian grids to Lagrangian particles. Therefore, the accuracy of the present solution will not be deteriorated by interpolation error. Additionally, no extra work is required to manage particles for searching procedure. Because no convection term needs to be discretized by upwinding schemes, false diffusion and dispersion errors will not be introduced, thereby increasing the solution accuracy. To verify the proposed particle method, several benchmark problems are solved to show that the present simulation is more stable, accurate, and efficient. The proposed particle method renders fourth- and second-order accurate solutions in space for velocity and pressure, respectively.",
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A new high-order particle method for solving high Reynolds number incompressible flows. / Liu, Rex Kuan Shuo; Ng, Khai Ching; Sheu, Tony Wen Hann.

In: Computational Particle Mechanics, Vol. 6, No. 3, 15.07.2019, p. 343-370.

Research output: Contribution to journalArticle

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